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Shadows Of The Circle: Conic Sections, Optimal Figures And Non-euclidean Geometry by Vagn Lundsgaard Hansen (Hardcover, 1998)

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This work offers insights on various facets of geometry through development of four geometric themes: ellipse, the shape or shadow cast by a cirlce; all three types of conic sections - the ellipse, the parabola and the hyperbola; certain properties of geometric figures related to the problem of finding the largest areas that can be enclosed by a curve of given length - the isoperimetric problem; and a development of the non-Euclidean geometry in the Poincare disc model of the hyperbolic plane.